Wave Propagation in a System of Coaxial Tubes Filled With Incompressible Media – A Model of Pulse Transmission in the Intracranial Arteries


  1. Cirovic, S.
  2. Walsh, C.
  3. Fraser, W.D.
Corporate Authors
Defence and Civil Inst of Environmental Medicine, Downsview ONT (CAN)
The propagation of harmonic waves through a system formed of coaxial tubes filled with incompressible continua is considered as a model of arterial pulse propagation in the craniospinal cavity. The inner tube represents a blood vessel and is modeled as a thin-walled membrane shell. The outer tube is assumed to be rigid to account for the constraint imposed on the vessels by the skull and the vertebrae. We consider two models in the first model the annulus between the tubes is filled with fluid; in the second model the annulus is filled with a viscoelastic solid separated from the tubes by thin layers of fluid. In both models, the elastic tube is filled with fluid. The motion of the fluid is described by the linearized form of the Navier-Stokes equations, and the motion of the solid by classical elasticity theory. The results show that the wave speed in the system is lower than that for a fluid-filled elastic tube free of any constraint. This is due to the stresses generated to satisfy the condition that the volume in the system has to be conserved. However, the effect of the constraint weakens as the radius of the outer tube is increased, and it should be insignificant for the typical physiological parameter range.
Report Number
DCIEM-SL--1999-077 — Scientific Literature
Date of publication
19 Aug 1999
Number of Pages
Reprinted from
Journal of Fluids and Structures, vol 16, no 8, 2002, p 1029-1049
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